Five phase machine

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Multi-criteria based design approach of multiphase permanent magnetlow speed synchronous machines

Journal: IET Electric Power Applications

Manuscript ID: EPA-2008-0003.R1

Manuscript Type: Research Paper

Date Submitted by theAuthor:

n/a

Complete List of Authors: Scuiller, Franck; Ecole Navale - Groupe des Ecoles du Poulmic,Institut de Recherche de l'Ecole NavaleSemail, Eric; Ecole Nationale Suprieure d'Arts et Mtiers, centre deLille, Laboratoire d'Electrotechnique et d'Electronique de PuissanceCharpentier, Jean-Frdric; Ecole Navale - Groupe des Ecoles duPoulmic, Institut de Recherche de l'Ecole NavaleLetellier, Paul; Groupe Altawest, Jeumont Electric

Keyword:AC MACHINES, BRUSHLESS MACHINES, PERMANENT MAGNETMOTORS, SYNCHRONOUS MOTORS

IET Review Copy Only

IET Electric Power Applications

hal008

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6Jun201

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Author manuscript, published in "Electric Power Applications, IET 3, 2 (2009) 102-110"DOI : 10.1049/iet-epa:20080003
http://dx.doi.org/10.1049/iet-epa:20080003http://hal.archives-ouvertes.fr/http://hal.archives-ouvertes.fr/hal-00817710http://dx.doi.org/10.1049/iet-epa:20080003


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Multi-criteria based design approach of multiphase

permanent magnet low speed synchronous machines

April 21, 2008

Abstract

This paper presents a design methodology dedicated to multiphase

Permanent Magnet Synchronous Machines (PMSM) supplied by Pulse

Width Modulation Voltage Source Inverters (PWM VSI). Firstly op-

portunities for increasing torque density using the harmonics are con-

sidered. The specific constraints due to the PWM supply of multiphase

machines are also taken into account during the design phase. All the

defined constraints are expressed in a simple manner by using a mul-

timachine modelling of the multiphase machines. This multimachine

design is then applied in order to meet the specifications of a marine

propeller: verifying simultaneously four design constraints, an initial

60-pole 3-phase machine is converted into a 58-pole 5-phase machine

without changing the geometry and the active volume (iron, copper

and magnet). Firstly, a specific fractional-slot winding, which yields

to good characteristics for PWM supply and winding factors, is cho-

sen. Then, using this winding, the magnet layer is designed to improve

the flux focussing. According to analytical and numerical calculations,

the five-phase machine provides a higher torque (about 15%) and less

pulsating torque (71% lower) than the initial three-phase machine with

the same copper losses.

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1 Introduction

Electrical marine propulsion commonly uses multiphase low speed motors

whose power is greater than 1MW. The number of phases, greater than

three, is not only justified by the induced power partition between the dif-

ferent phases but also by a smoother torque and a higher fault tolerance.

With the advances of Digital Signal Processors (DSP) and high power de-

vices such as Insulated Gate Bipolar Transistors (IGBT), it is now possible

to use PWM VSI for supplying high power propulsion machines [1]. The

induction machines and the PMSM can be easily considered in this instance

since the constraint on the reactive power does not apply [2].

PMSM with rare earth magnets are an expensive solution but present

an even higher torque density than the induction machines, especially by

making use of the harmonics of the electromotive force (emf) in the case

of multi-phase machines. This point is very interesting for ship propulsion

podded motors and for submarine motors [3]. Nevertheless, the torque rip-

ples, of critical importance for low speed motors, become then more difficult

to control because of the interactions of the current with the harmonics of

the emf.

Even though, for cases where very high power values are used (greater

than 10MW), the use of multi-phase machines is still justified due to the

distribution of power, this is not necessarily valid for medium power [4].

Of course, the tolerance to faults as in open-circuited phases is still higher

with multiphase machines. On the contrary, the torque pulsations of the

three-phase machines can be very low if they are controlled in the rotor d-q

reference frame and if their emfs are sinusoidal [5]. If the emfs are not sinu-

soidal and a classical vector control with simple Intersective PWM is used,

then interactions between emf harmonics and the fundamental of the current

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induce torque pulsations. One major advantage of multiphase PM machines

is to alleviate this constraint related to sinusoidal emfs, by taken advantage

of the harmonics of electromotive forces. The torque density (in Nm/m3)

can be higher than with three-phase sinusoidal machines while keeping the

same quality of torque [6]. This offers new opportunities when determin-

ing the winding configurations [7, 8] and for the shapes of the Permanent

Magnet.

This paper presents different criteria that are taken into account simulta-

neously for the design of a multiphase low speed PMSM in order to improve

performance. Our work focuses on acting on the space harmonics whose in-

teractions are different for a multi-phase machine in comparison with those

of a three-phase machine. It has been shown, initially for particular mul-

tiphase machines with concentrated windings [9], and more recently for a

wider family of n-phase machines [10] with N identical and regularly shifted

windings, that families of space harmonics can be defined. These familiesdo not interact amongst themselves.

The criteria of this methodology are firstly presented. This method is

then applied to increase the performance of a 2.1MW podded propeller: the

initial design using a three-phase PMSM is transformed into a five-phase

one that fulfills all the specified criteria. The transformation is obtained

by a small modification of the pole number and the use of fractional slot

unconventional windings. The last part of the study shows that the motor

performances can be improved further by changing the magnet layer. This

change optimizes the use of the first and third emf harmonics to increase

the torque density.

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2 Design approach for five-phase PM machines

2.1 Criteria to improve the torque density of a five-phase

machine with references to a three-phase machine

In this subsection, our aim is to find a simple condition that ensures a torque

density improvement when the phase number is changed from three to five,

with the assumption of a perfect sinusoidal current. These two machines are

assumed to have the same main geometrical specifications (same diameter)

and to run with the same current density js, the same linear load A and the

same active volume of copper Vcu. Consequently the copper sections Scu are

also equal. In other words, the two machines have the same active copper

losses and the same thermal behaviour.

Given the perfect sinusoidal current assumption, the average electromag-

netic torque provided by a N-phase machine results from the interaction

of the phase current and the back-emf fundamental. The average torque

Tavg(N) is then equal to the product of the RMS value of the current

iRMS(N) by the RMS value of the elementary back-emf RMS(N) :

Tavg(N) = NRMS(N)iRMS(N)cos() (1)

In (1), is the angle between the current and the back-emf. In (1), we can

replace the RMS current density js and the conductor section scd(N):

Tavg(N) = NRMS(N)jsscd(N)cos()

The conductor section scd(N) is also the total copper section Scu divided by

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the total number of conductors ncd(N):

Tavg(N) = jsScu

ncd(N)NRMS(N)cos()

The total number of conductors ncd(N) can be expressed as the product of

the phase number N by the number of conductors per phase ncd/(N):

Tavg(N) = jsScu

Nncd/(N)NRMS(N)cos()

The elementary back-emf for a conductor RMScd (N) is thus given by:

Tavg(N) = jsScuRMScd (N)cos() (2)

Relation (2) allows us to define the condition necessary to obtain a higher

average torque with a five-phase machine than with a three-phase machine.

This condition, which we called (C1), is related to the associated elementary

back-emf for a conductor:

Tavg(5)

Tavg(3) 1

RMScd (5)

RMScd (3) 1 (3)

With this condition (C1), the five-phase machine is guaranteed a higher aver-

age torque than the three-phase machine when using the classical sinusoidal

supply strategy. Moreover, if the third harmonic current injection and the

design strategy described in the next subsection are used, the performance

becomes even better.

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2.2 Criteria based on the harmonic property of the multi-

phase machines

In this paragraph, we define two criteria (C2) and (C3) that are directly

linked with the presence of independent families of harmonics for a machine

that fulfills the following assumptions [10]:

the five phases are identical and regularly shifted

saturation and damper windings are neglected

the back electromotive force (back-EMF) in the stator windings is not

disturbed by the stator currents.

For a wye-coupled five-phase machine, two families must be thus considered.

One way to give a synthetic view of a multi-phase machine is to consider it

as a set of two 2-phase fictitious machines noted M1 and M2, electrically and

mechanically coupled, each characterized by its own cyclic inductance andback electromotive force. The total torque is the sum of the two elementary

torques produced by the M1 and M2. Each elementary machine is associated

with a particular family of harmonics (M1, 1st, 9th, (10k 1)th harmonics;

M2, 3rd, 7th, (10k 3)th harmonics). As such, a simple but efficient vector

control using a VSI can be implemented for this machine if the following

appropriate criteria are satisfied during the design for the two fictitious

machines:

(C2): the two cyclic inductances 1 and 2 of the same order

(C3): two sinusoidal electromotive forces.

To explain the origin of the (C2) criterium, let us note that if the machine

has a pure sinusoidal mmf, then the cyclic inductance 2 of M2 is only

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determined by the leakage flux. As the time constants are 1 = 1/Rs and

2 = 2/Rs, with Rs the stator resistance, it is easy to understand that the

amplitude of the parasitic currents induced by the PWM will be limited by

the choice of a high carrier-frequency. It is then convenient to design the

machine in order to have the same order for the two cyclic inductances. To

fulfill this objective, it is possible to act on the windings. Windings with

magnetomotive forces of the same value for the first and third harmonics

imply two identical cyclic inductances. Consequently, it is necessary to

conceive adequate windings. The criterium (C3) regarding the electromotive

force can be satisfied by changing the windings and the magnet layer.

Finally, a machine satisfying these two properties can then develop a

perfectly constant torque when it is supplied by currents that contain only

the first and the third harmonics. Thus the third harmonic of the emf con-

tributes to a higher torque without additional torque ripples. It is possible

to design machines that can rotate at very low speeds without vibrations in-duced by torque ripples. Of course, a fourth design criterium (C4) concerns

the cogging torque.

3 Conversion of a three-phase machine into a five-

phase machine

By considering the design of a podded propeller (2100 kW at 105 rpm), this

section practically illustrates the benefits that can be expected when using

these specifications with a phase number equal to 5 instead of 3. The spec-

ifications given in table 1 correspond to the characteristics of the reference

three-phase propeller. All these characteristics remain invariant when the

phase number is changed to 5. Particularly, iron, magnet and active cop-

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Table 1: Propeller characteristicsEffective length 1.125 m

Stator diameter D 1.6 m

Stator yoke thickness 0.05 m

Mechanical airgap g 0.005 m

Rotor yoke thickness 0.03 m

Magnet layer thickness 0.015 m

Remanent flux density Br 1.17 T

Magnet volume 83.5 103m3

Slot width (s, tooth pitch) 0.5 sSlot width opening 0.25 s

Slot-closing thickness 0.005 mSlot depth 0.065 m

Active copper volume Vcu 95.6 103m3

Linear load A 6.17 104 A/m

Current density js 3.65 106 A/m2

per volumes remain invariant. To convert the three-phase machine into a

five-phase one, only the numbers of slots and poles are changed to make a

five-phase winding feasible.

3.1 Initial machine analysis

The initial machine has 216 slots and 60 poles. Therefore the number of

slots per phase and pole for this 3-phase winding is spp = 6/5. Each pole is

made of a fully pitched radial magnet with a 1.17 T remanent magnetic flux

density. The pole-slot arrangement yields a fractional-slot winding, which

provides an efficient mean of reducing the cogging torque [11]. The funda-

mental winding factor is 0.927. This three-phase machine is wye-coupled.

Therefore the third back-emf harmonic can not be used to produce addi-

tionnal torque. According to 2D numerical prediction, the time constant

of the elementary machine is about 0.112 s. Considering this value and the

nominal speed of 105 rpm, a PWM frequency of 1000 Hz ensures a low level

of parasitic current for the entire speed range [12].

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3.2 Five-phase winding requirements

To convert the three-phase machine into a more efficient five-phase one, it

is necessary to find a new fractional slot winding that fulfills the following

conditions:

relation (3) regarding the average torque must be verified (condition

C1)

the time constants of both elementary machines must be compatible

with the PWM frequency of 1000 Hz (condition C2)

the third harmonic winding factor must be as high as possible in order

to enable the M2 machine to provide a significant torque (condition

C3)

the cogging torque should not be increased when using the new pole-

slot configuration (condition C4).

The new slot number must be a multiple of the phase number and the new

pole number must remain near enough to the initial value of 60 in order to

roughly maintain the same current frequency. It is possible to obtain a five-

phase winding with 60 poles and 200 slots but this configuration clearly does

not fulfill the condition C4 regarding the cogging torque. Indeed, according

to [11], with this configuration, the first flux density harmonic contribution

becomes the 5th whereas it is the 9th with the initial three-phase winding.

This solution is thus rejected.

3.3 Method used to study the winding

To take full advantage of the opportunity offered by the Permanent Mag-

net synchronous machines, fractional slot windings which have already been

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studied for three-phase machines [13], are again considered for fault tol-

erant [14] and multi-phase machines [8]. In this paper, the procedure to

determine a convenient 5-phase winding is deduced from [15]. If the phase

number, the pole number and the phase number are known, it is possible to

deduce a set of coils per phase that leads to balanced multi-phase windings.

The procedure is divided into four steps. The first step involves initializ-

ing the procedure: it consists of selecting a set of coils per phase that will

be examined. The number of selected coils is Ns/(2N) because only single

layer windings are explored. The following step verifies that the selected

coils yields a feasible winding. The third step concerns the condition C2

regarding the time constants of the 2-phase elementary machines that must

be of the same order. The fourth step takes into account the winding factor

requirements (condition C3). For each step, if the criteria is not satisfied,

the coils selection is rejected and a new selection is examined. Fulfilment

of conditions C1 and C4 directly depends on the choice of the pole and slotnumbers.

3.4 New five-phase winding

By using the above procedure, it is possible to find a convenient five-phase

winding with 180 slots if the pole number is decreased to 58. Each phase is

made up of 18 coils. In figure 2, phase 1 winding is represented. The number

of slots per phase and per pole for this 5-phase winding is spp = 18/29. The

phase 2 winding is shifted 36 slots forward with the phase 1 winding.

In order to determine the electrical quantities, two tools are available:

an analytical 2D field calculation software program based on [16] and the

numerical 2D software Difimedi [17]. Both of these have been successively

used. For example, figure 3 shows the magnetic flux distribution when one

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phase is supplied with a constant current obtained with the numerical 2D

software. Thus the inductances values and the back-EMF are first ana-

lytically estimated and then controlled using the numerical software. The

stator resistances are calculated by considering the conductor section and

the length for average temperature. The electrical time constant can thus

be estimated. All the conditions are fulfilled for this machine.

As shown in figure 4 which compares the two elementary back-emfs for

a conductor, condition C1 is verified:

RMScd (5)

RMScd (3)= 1.054

Consequently the five-phase machine enables us to provide a better average

torque than the three-phase one when using sinusoidal supply.

Furthermore, condition C2 is also fulfilled:

1 = 0.152 s and 2 = 0.106 s

These values are both obtained by 2D analytical and numerical calculations.

The difference is about 5% higher for 1 and 9% higher for 2 with the

analytical software. The PWM frequency of 1000 Hz thus remains sufficient

to ensure low parasitic currents.

Condition C3 regarding the winding factors is also satisfied: the funda-

mental winding factor rises from 0.927 to 0.984 while the third harmonic one

is equal to the satisfactory value of 0.859, which makes the torque produced

by the M2 elementary machine valuable (if the flux density produced by the

rotor contains a significant part of the third harmonic).

Finally, concerning condition C4, this new pole-slot configuration guar-

antees a negligible cogging torque since the first flux density harmonic con-

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tribution is the 45th. As underlined in the previous section which introduced

the multimachine design, the multiphase topology enables a better use of

the magnet volume. This aspect is illustrated in the second section which

deals with the issue of magnet layer optimisation.

4 Magnet layer optimisation

For given geometrical dimensions (stator diameter, mechanical airgap, mag-

net layer thickness and slot parameters), the back-emf depends on two design

elements: on the one hand, the winding studied in the previous section; on

the other hand, the rotor geometry examined in this section. This section

looks at magnet layer adaptation to the multimachine supply strategy in

order to improve the torque density.

4.1 Multimachine design requirements regarding magnet layer

With regards to the windings, the ideal rotor structure is the one that only

generates the first harmonic of each 2-phase elementary machine (first har-

monic for M1 and third one for M2). In this way, each elementary machine

has a sinusoidal back-emf and can provide a constant torque in the case of

multimachine supply (as explained previously in 2.2). For the given five-

phase machine, it is interesting to look for a particular magnet layer that

favours first and third harmonics in the back-emf spectrum. Furthermore,

according to the sinusoidal back-emf objectives for the two elementary ma-

chines, the other back-emf harmonics that belong to the two harmonic famil-

lies (see figure 1) must be as weak as possible: the torque ripples are equal

to zero if these conditions are fulfilled. In practise, for the M1 elementary

machine, harmonic 1 (the fundamental) must be high and harmonics 9 and

11 low; for the M2 machine, harmonic 3 must be high and harmonics 7 and

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13 low. For the given machine, owing to the large airgap effect that reduces

high order flux density harmonic and the corresponding winding factors that

filter harmonics 7, 9, 11 and 13, this constraint is naturally respected.

4.2 Problem analysis

For the given machine, as the winding is chosen, the only way to act on the

back-emf spectrum is to modify the no load airgap flux density waveform.

The objective is to increase the first and third harmonics in comparison with

respect to initial propeller configuration where the pole consists of a fully

pole pitched radial magnet. It should be noticed that such a pole configura-

tion allows us to obtain a higher value for the airgap flux density than the

one obtained with the more classical configuration where the magnet arc to

pole pitch ratio is about 2/3. This second configuration is not convenient in

this instance because the back-emf third harmonic that is required by the

M2 elementary machine to produce torque is null. The fully pole pitched

configuration is thus more interesting since the no load airgap flux density

contains both first and third harmonics. Unfortunately this improvement

comes with an increase in the interpolar flux density leakage. For the ma-

chines with high airgap to pole pitch ratios, the fully pole pitched radial

magnet configration leads to important interpolar leakage flux, which can

be considered as an inefficient use of the magnet volume.

The approach proposed in this section is to change the pole magnet layer

characteristics in order to obtain a more convenient airgap flux density than

the one corresponding to the initial magnet layer (fully pole pitched). The

optimised magnet layers must provide an airgap flux density spectrum with

higher 1st and 3rd harmonics than in the initial case. Reaching this goal is

equivalent to reducing the interpolar flux density leakage, leading to better

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use of the magnet volume.

4.3 Method

It is decided to look for a pole composed of three magnets with parallel

magnetisation. All the magnets have the same magnetisation value. This

approach is comparable to the segmented Halbach array path, so called flux

focussing technology [18]. Due to the hypothesis of pole symmetry, the intro-

duction of two design parameters is sufficient to formulate the optimisation

variable:

the length of the adjacent magnet L can vary from 0to 90(electrical

degrees)

the orientation angle of the magnetisation of the adjacent magnet

can vary from -90to 0

These two parameters define the optimisation variable x = (L, ). They

are depicted in figure 5. By using a rather precise analytical flux density

calculation [16], the flux density spectrum for the five-phase machine with

poles made of fully pitched radial magnets can be estimated (and controlled

with the numerical calculation tool Difimedi). The 1st and 3rd harmonic

amplitudes take the following values:

Bref1 = 1.04 T and Bref3 = 0.52 T

The optimised magnet layer must improve on these two values. The solution

x must thus satisfy the following condition:

B1(x)

Bref1 1 and

B3(x)

Bref3 1 (4)

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The speed and the sufficient accuracy of the analytical calculation method

make the estimation of these two ratios possible for numerous values of

x. The results are presented by the figure 6. The best improvements for

the fundamental and the third harmonic are respectively about 5.9% and

28.5%. As these maximal values are not reached for the same point x,

a compromise must be realized: it consists in choosing the point x that

leads to the better average torque with the multimachine supply strategy.

By taking into account the winding factors and the slot parameters, the

fundamental and third-harmonic back-emf can be estimated, which allows

the prediction of the EM torque. So it can be shown that the better point

is:

xopt = (0.29 elec/2,47 deg) =

B1(xopt)

Bref1

= 1.056

B3(xopt)

Bref3

= 1.238

The figure 6 also shows the point xhal that corresponds to the Halbach array

solution (the Halbach array with three magnets per pole). This solution

is less interesting because the third harmonic is significantly lower (1.196

for xhal againt 1.238 for xopt) whereas the fundamental has the same level

(1.057 for xhal against 1.056 for xopt). It can be noticed that, as an Halbach

Array, the chosen topology partially focuses the PM magnetic flux in the

magnet layer. So, with this configuration, the back iron core thickness can be

reduced from 30mm to 18mm according to the numerical software Difimedi.

4.4 Results

Concerning the back-emf waveform, the figure 7 compares the elementary

machines back-emf for the radial magnet five-phase machine with the opti-

mised ones (for the same active volume). The analytical results, confirmed

by the 2D numerical ones, are really satisfying: the amplitudes are higher

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Table 2: Analytical results concerning the torque improvementMachine Magnet layer Supply Avg torque Torque ripples

3-phase Conventional sinus T0 t03-phase Optimised sinus 1.06T0 0.95 t05-phase Conventional sinus 1.05T0 0.64 t05-phase Optimised sinus 1.11T0 0.02 t05-phase Optimised 1 & 3 1.15T0 0.29 t0

and the signals are more sinusoidal. The back-emf first harmonic is in-

creased by 5.5% and the third harmonic back-emf by 23%. In comparison

with the initial three-phase machine, the fundamental improvement is more

than 11.2%. Obviously this comparison is more pertinent if the magnet

layer optimisation method is also used for the three-phase machine. In this

case (where the optimal point is x = (0.43elec/2,39 deg)), the results

remain convincing: the increase is about 4.8% (mainly due to the better

fundamental winding factor of the five-phase machine).

The wye coupled three-phase machine however can not use the back-emf

third harmonic to provide torque. This explains why the EM torque pro-

vided by the five-phase machine with the optimised magnet layer is always

higher than the one produced by the three-phase machine even if its mag-

net layer is also optimised. This assertion is illustrated by figure 8, which

represents the EM torque produced by the different machine configurations.

The reduction of the pulsating torques for the five-phase machine is quite

clear. The results, according to analytical predictions, are summarized in

table 2 which provides values for the average torque and the torque ripples

(maximum minus minimum) with respect to the initial three-phase machine

where T0 = 191 kNm and v0 = 2.13 kNm. It can be noticed that, for the

optimised magnet layer five-phase machine, the sinusoidal supply is suffi-

cient to obtain an improved EM torque with regards to the amplitude and

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ripples. Concerning this point, it is logical to obtain additionnal ripples

when the M2 machine is supplied to produce torque: the phenomenon re-

sults from the harmonic interaction between the third harmonic current and

the back-emf harmonics that belong to the corresponding harmonic familly

(7, 13, ...). However the level of ripples remains low in comparison with the

initial value.

5 Conclusion

Given that the multimachine approach provides a synthetic view of the

multiphase machines in terms of both control and design, it is possible to

consider the number of phases as a design parameter of a drive. Specific

example of an application of this principle has been given in this paper re-

lated to a marine propeller where the torque density and the torque ripples

are of critical importance and the fault tolerance appreciated. Design ob-

jectives for the electrical time constants and the emf spectrum have been

identified. The choice of an adapted fractional slot five-phase winding and

the optimisation of the magnet layer characteristics significantly improve

the torque quality, in comparison with the initial three-phase configuration,

and increase the fault tolerance. Particularly, the five-phase topology al-

lows better use of the magnet volume. Of course, this advantage for the

machine could be tempered by the apparent need for a higher number of

switching devices. In fact, this must be carefully studied because, for high

power, a switch is often a combination, in series and/or parallel, of elemen-

tary semiconductor devices. In this case, the tolerance to semiconductor

device breakdown appears to be more even advantageous with multiphase

machines.

Despite the promising nature of the results, two main drawbacks must

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be considered. First, the simulations used in this paper are based on 2D field

calculations, which means that end-turn effects are not taken into account.

The mutual phase fluxes related to the end-turns and the estimation of the

required copper length are not carried out. However the pulsating torque

reduction is guaranteed. The other moderating argument concerns the mag-

netomotive force distribution generated by the new five-phase winding. As

the MMF subharmonics can induce mechanical stresses [19], it would be

useful to assess their influence. To summarize, the expected benefits of the

five-phase topology need to be more accurately estimated.

References

[1] E. Levi, E. Bojoi, F. Profumo, H. Toliyat, and S. Williamson, Multi-

phase induction motor drives - a technology status review. IET Electric

Power Applications, vol. 1, no. 4, pp. 489516, 2007.

[2] P. Letellier, High power permanent magnet machines for electric

propulsion drives, in Proc. of the All Elctric Ship Symposium, Paris,

France, 26-27 october 2000, pp. 126132.

[3] A. Arkkio, N. Bianchi, S. Bolognani, T.Jokinen, F. Luise, and M.Rosu,

Design of synchronous pm motor for submersed marine propulsion

systems, in Proc. of International Congress on Electrical Machines

(ICEM02), CD-ROM, Brugges (Belgium), August 2002.

[4] P. Norton and P. Thompson, The naval electric ship of today and

tomorrow, in Proc. 3rd All Electric Ship Symp, Paris, France, 26-27

october 2000, pp. 8086.

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[5] T. Lipo and K. Jezernik, AC Motor Speed Control, chap 15. Electric

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6 Figures

Figure 1: Multimachine decomposition for a wye-coupled 5-phase machine

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New 5phase machine180 slots and 58 poles

Figure 2: Winding configuration of a phase for the 5-phase machine

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Figure 3: Magnetic flux distribution when one phase is supplied with aconstant current (new machine) according to the numerical 2D software

0 30 60 90 120 150 180 210 240 270 300 330 3601

0.8

0.6

0.4

0.2

0

0.2

0.4

0.6

0.8

1

Electrical Angle (deg)

Elementaryback

EMFbyconductor(V)

3phase backEMF3phase backEMF fundamental5phase backEMF5phase backEMF fundamental

Figure 4: Comparison of the elementary back-EMF by conductor cd(3) andcd(5) (analytical estimations)

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Figure 5: Modification of the magnet layer

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 190

80

70

60

50

40

30

20

10

0

1

1

1

1.02

1.02

1.02

1.021.02

1.02

1.02

1.02

1.041.04

1.04

1.04

1.04

1.04

1.04

1.04

1.05

1.05

1.05

1.05

1.051.055

1.0551.055

xopt

xhal

L / (elec

/2)

B1(x) / B

1

ref

(a) Fundamental flux density change

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 190

80

70

60

50

40

30

20

10

0

1

1

1

1

1

03

03

.03

1.03

1.03

1.03

1.03

1.03

.06

1.06

1.06

1.06

1.06

1.06

1.061.09

1.09

1.09

1.09

1.09

1.09

1.09

1.12

1.12

1.12

1.12

1.12

1.12

1.15

1.15

1.15

1.15

1.15

1.15

1.18

1.18

1.18

1.18

1.18

1.18

1.21

1.21

1.21

1.211.24

1.24

1.24

1.24

1.27

1.27xopt

xhal

L / (elec

/2)

B3(x) / B

3

ref

(b) Third harmonic flux density change

Figure 6: Flux density change with optimisation variable (L, )

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0 30 60 90 120 150 180 210 240 270 300 330 3601

0.8

0.6

0.4

0.2

0

0.2

0.4

0.6

0.8

1

Electrical Angle (deg)

Elementaryback

EMF(V)

Radial Magnet 5phase machine: Main MachineOptimised 5phase machine: Main MachineRadial Magnet 5phase machine: Secondary MachineOptimised 5phase machine: Secondary Machine

Figure 7: Elementary machine back-EMF improvement (analytical estima-tion)

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0 2 4 6 8 10 121.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

2.25

2.3x 10

5

Mechanical Angle (deg)

EMt

orque(Nm)

M3, radial magnetsM3, optimised magnetsM5, radial magnets, sinusoidal supply

M5, optimised magnets, sinusoidal supplyM5, optimised magnets, multimachine supply

Figure 8: EM torques comparison for the 3-phase and 5-phase machineswith conventional and unconventional magnets layer

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